Objectives –
Recognize characteristics of parabolas 

Quadratic functions, f(x)=ax^{2} +bx + c graph to be a parabola. 
Parabola • Parabolas
are 

Special Factored Form of the Quadratic Equation • The vertex of the parabola is at (h,k) and “a” describes the “steepness” and direction of the parabola given by the form f (x) = a(x − h)^{2} + k 
Minimum or maximum values of a function occur at the VERTEX.
a > 0
parabola opens up (h,k) = minimum point 

Minimum (or maximum) function value for a quadratic occurs at the vertex. • If parabola opens up, f(x) has a minimum value. • If it opens down, f(x) has a maximum value. • Minimum/Maximum values are based on yvalues. 
Graph of f (x) = 2x^{2} − 4x + 3 = 2(x −1)^{2}


Vertex Formula P(x) = ax^{2} + bx + c (a ≠ 0) The following formula will give you the xvalue for the vertex of a quadratic:
Coordinates of vertex: 
Example • Determine the following for f(x) without graphing. • f(x) = 3(x – 2)² + 12 a.) Find the vertex. b.) Find the equation of the axis of symmetry. c.) Does f(x) open up or down? d.) Does f(x) have a max. or min. value? Where does this value occur? e.) What is the domain of f(x)? f.) What is the range of f(x)? 

Example • Determine the following for f(x) without graphing. • f(x) = 2x²  8 x  3 a.) Find the vertex. b.) Find the equation of the axis of symmetry. c.) Does f(x) open up or down? d.) Does f(x) have a max. or min. value? Where does this value occur? e.) What is the domain of f(x)? f.) What is the range of f(x)? 
To Graph a Quadratic Function 1. Find the coordinates of the vertex. (Use the vertex formula.) 2. Determine which way parabola opens by looking at a. a > 0 parabola opens up (Vertex is lowest point) a < 0 parabola opens down (Vertex is highest point) 3. Find the xintercept(s). (Set y = 0) 4. Find the yintercept. (Set x = 0) 2. Graph additional points if needed by tchart or symmetry. 

Use the vertex and intercepts to graph f(x) = 5 – 4x – x² Give the equation of the axis of symmetry. Determine the domain and the range of f(x).
